$g(t) = 4t^{2}+t+2(f(t))$ $f(t) = -4t+6$ $h(x) = 6x^{2}+5(g(x))$ $ f(h(0)) = {?} $
First, let's solve for the value of the inner function, $h(0)$ . Then we'll know what to plug into the outer function. $h(0) = 6(0^{2})+5(g(0))$ To solve for the value of $h$ , we need to solve for the value of $g(0)$ $g(0) = 4(0^{2})+2(f(0))$ To solve for the value of $g$ , we need to solve for the value of $f(0)$ $f(0) = (-4)(0)+6$ $f(0) = 6$ That means $g(0) = 4(0^{2})+(2)(6)$ $g(0) = 12$ That means $h(0) = 6(0^{2})+(5)(12)$ $h(0) = 60$ Now we know that $h(0) = 60$ . Let's solve for $f(h(0))$ , which is $f(60)$ $f(60) = (-4)(60)+6$ $f(60) = -234$